arXiv subjects

Zhijie Xu

Publications and source records attributed to Zhijie Xu.

At least 37 records · Page 2Linked to original sources

arXiv2023

Scientific Computing Algorithms to Learn Enhanced Scalable Surrogates for Mesh Physics

Data-driven modeling approaches can produce fast surrogates to study large-scale physics problems. Among them, graph neural networks (GNNs) that operate on mesh-based data are desirable because they possess inductive biases that promote physical faithfulness, but hardware limitations have precluded their application to large computational domains. We show that it is \textit{possible} to train a class of GNN surrogates on 3D meshes. We scale MeshGraphNets (MGN), a subclass of GNNs for mesh-based physics modeling, via our domain decomposition approach to facilitate training that is mathematically equivalent to training on the whole domain under certain conditions. With this, we were able to train MGN on meshes with \textit{millions} of nodes to generate computational fluid dynamics (CFD) simulations. Furthermore, we show how to enhance MGN via higher-order numerical integration, which can reduce MGN's error and training time. We validated our methods on an accompanying dataset of 3D $\text{CO}_2$-capture CFD simulations on a 3.1M-node mesh. This work presents a practical path to scaling MGN for real-world applications.

cs.LG↗

arXiv2023

Direct effect of solvent viscosity on the physical mass transfer for wavy film flow in a packed column

The interphase mass transfer plays a critical role in determining the height of packed column used in the absorption process. In a recent experiment (Song D. Ind. Eng. Chem. Res. 2018, 57, 718), the direct impact of viscosity ($μ_L$) on the physical mass transfer coefficient ($k_L$) was observed to be higher in a packed column as compared to the wetted wall column. We offer a plausible mechanism involving the wavy film and eddy enhanced mass transfer in a packed column to explain the underlying physics via analytical and numerical studies. The analytically derived mass transfer coefficient matches well with experimental observation in a packed column. The countercurrent flow simulations in a packed column with both uniform and wavy films also confirm this behavior. The predicted $k_L$ shows steep variation with $μ_L$ for a wavy film than a uniform film and further confirms the proposed theory. A similar relation ($k_L \propto μ_L^{-0.38}$) for a wavy film is also observed in theoretical, experimental, and numerical studies.

physics.flu-dyn↗

arXiv2022

Hydrodynamics of countercurrent flows in a structured packed column: effects of initial wetting and dynamic contact angle

Computational countercurrent flow investigation in the structured packed column is a multiscale problem. Multiphase flow studies using volume of fluid (VOF) method in the representative elementary unit (REU) of the packed column can insight into the local hydrodynamics such as interfacial area, film thickness, etc. The interfacial area dictates the mass transfer in absorption process and thereby overall efficiency of column. Impacts of solvent's physical properties, liquid loads and static contact angle (SCA) on the interfacial area were examined earlier. In the present study, the dynamic contact angle (DCA) was used to explore the impact of contact angle hysteresis on the interfacial area. DCA has more pronounced impact on the interfacial area (10%) for aqueous solvent of 0.10M Sodium hydroxide (NaOH). The interfacial area shows undulation and does not achieve the pseudo-steady state. In contrary, the interfacial area gets a net pseudo-steady value for the aqueous solvent having 40% monoethanolamine (MEA) by weight. The wetting hysteresis was also explored via simulations conducted with initially dry and wetted sheets. For 0.10M NaOH aqueous solvent, the initially wetted sheets lead to slightly higher value of the interfacial area (10%) as compared to the initially dry sheets at the same liquid load and DCA. As expected, wetting hysteresis reduces with increasing liquid loads. On the other hand, wetting hysteresis is not significant for 40% MEA aqueous solvent which might be lower surface tension and higher viscosity. Overall, the effect of the dynamic contact angle is not pronounced as compared to those found in a flat surface.

physics.flu-dyn↗

arXiv2022

The baryonic-to-halo mass relation from mass and energy cascade in self-gravitating collisionless dark matter flow

The relation between properties of galaxies and dark matter halos they reside in can be valuable for structure formation and evolution. This paper focus on the baryonic-to-halo mass ratio (BHMR) and its evolution. We first review unique properties of self-gravitating collisionless dark matter flow (SG-CFD), followed by their application to derive BHMR. To maximize system entropy, the long-range interaction requires a broad size of halos to be formed. These halos facilitate inverse mass and energy cascade from small to large scales with a constant rate of energy cascade $\varepsilon_u$. In addition, dark matter flow exhibits scale-dependent flow behaviors that is incompressible on small scale and irrotational on large scale. With these properties and considering a given halo with a total baryonic mass $m_b$, halo mass $m_h$, halo virial size $r_h$, and flat rotation speed $v_f$, BHMR can be analytically derived by combining the baryonic Tully-Fisher relation and constant $\varepsilon_u$ in small and large halos. A maximum BHMR ratio ~0.076 is found for halos with a critical mass $m_{hc}\sim 10^{12}M_{\odot}$ at z=0. That ratio is much lower for both smaller and larger halos such that two regimes can be identified: i) for incompressible small halos with mass $m_h m_{hc}$, we have $\varepsilon_u\propto v_f^3/r_h$, $v_f\propto r_h^{1/3}$, and $m_b\propto m_h^{4/9}$. Combined with double-$λ$ halo mass function, the average BHMR ratio in all halos (~0.024 at z=0) can be analytically derived, along with its redshift evolution. The fraction of total baryons in all galaxies is ~7.6% at z=0 and increases with time $\propto t^{1/3}$. The SPARC (Spitzer Photometry \& Accurate Rotation Curves) data with 175 late-type galaxies were used for derivation and comparison.

astro-ph.GA↗

arXiv2022

Evolution of energy, momentum, and spin parameter in dark matter flow and integral constants of motion

N-body equations of motion in comoving system and expanding background are reformulated in a transformed system with static background and fixed damping. The energy and momentum evolution in dark matter flow are rigorously formulated for both systems. The energy evolution in transformed system has a simple form that is identical to the damped harmonic oscillator. The cosmic energy equation can be easily derived in both systems. For entire N-body system, 1) combined with the two-body collapse model (TBCM), kinetic and potential energy increase linearly with time $t$ such that $K_p=\varepsilon_ut$ and $P_y=-7\varepsilon_ut/5$, where $\varepsilon_u$ is a constant rate of energy cascade; 2) an effective gravitational potential exponent $n_e=-10/7\ne-1$ ($n_e=-1.38$ from simulation) can be identified due to surface energy of fast growing halos; 3) the radial momentum $G\propto a^{3/2}$ and angular momentum $H\propto a^{5/2}$, where $a$ is the scale factor. On halo scale, 1) halo kinetic and potential energy can be modelled by two dimensionless constants $α_s^*$ and $β_s^*$. Both constants are independent of time and halo mass; 2) both halo radial and angular momentum $\propto a^{3/2}$ and can be modeled by two mass-dependent coefficients $τ_s^*$ and $η_s^*$; 3) halo spin parameter is determined by $α_s^*$ and $η_s^*$ and decreases with halo mass with derived values of 0.09 and 0.031 for small and large halos. Finally, the radial and angular momentum are closely related to the integral constants of motion $I_m$, i.e. the integral of velocity correlation or the $m$th derivative of energy spectrum at long wavelength limit. On large scale, angular momentum is negligible, $I_2$=0 reflects the conservation of linear momentum, while $I_4$ reflects the fluctuation of radial momentum $G$. On halo scale, $I_4$ is determined by both momentum that are comparable with each other.

astro-ph.CO↗

arXiv2022

Two-body collapse model for self-gravitating flow of dark matter and generalized stable clustering hypothesis for pairwise velocity

Analytical tools are extremely hard to find for non-linear gravitational collpase. Only a few simple but powerful tools exist so far. Two examples are the spherical collapse model (SCM) and stable clustering hypothesis (SCH). We present a new analytical tool, a two-body collapse model (TBCM), that plays the same fundamental role as harmonic oscillator in dynamics. For convenience, TBCM is formulated for gravity with any potential exponent $n$ in a static background with a fixed damping ($n$=-1 for Newtonian gravity). The competition between gravity, expanding background (or damping), and angular momentum classifies two-body collapse into: 1) free fall collapse, where free fall time is greater if same system starts to collapse at earlier time; 2) equilibrium collapse that persists longer in time, whose perturbative solutions lead to power-law evolution of system energy and momentum. Two critical values $β_{s1}=1$ and $β_{s2}=1/3π$ are identified that quantifies the competition between damping and gravity. Value $β_{s2}$ only exists for discrete values of potential exponent $n=(2-6m)/(1+3m)=$ -1,-10/7... for integer $m$. Critical density ratio ($Δ_c=18π^2$) is obtained for $n$=-1 that is consistent with SCM. TBCM predicts angular velocity $\propto Hr^{-3/2}$ for two-body system of size $r$. The isothermal density is a result of extremely fast mass accretion. TBCM is able to demonstrate SCH, i.e. mean pairwise velocity (first moment) $\langleΔu\rangle=-Hr$. A generalized SCH is developed for higher order moments $\langleΔu^{2m+1}\rangle=-(2m+1)\langleΔu^{2m}\rangle Hr$ that is validated by N-body simulation. Energy evolution in TBCM is independent of particle mass and energy equipartition does not apply. TBCM can be considered as a non-radial SCM. Both models predict the same critical density ratio, while TBCM contains much richer information.

astro-ph.CO↗

arXiv2022

The mean flow, velocity dispersion, energy transfer and evolution of rotating and growing dark matter halos

By decomposing velocity dispersion into non-spin and spin-induced, mean flow and dispersion are analytically solved for axisymmetric rotating and growing halos. The polar flow can be neglected and azimuthal flow is directly related to dispersion. The fictitious ("Reynolds") stress acts on mean flow to enable energy transfer from mean flow to random motion and maximize system entropy. For large halos (high peak height $ν$ at early stage of halo life) with constant concentration, there exists a self-similar radial flow (outward in core and inward in outer region). Halo mass, size and specific angular momentum increase linearly with time via fast mass accretion. Halo core spins faster than outer region. Large halos rotate with an angular velocity proportional to Hubble parameter and spin-induced dispersion is dominant. All specific energies (radial/rotational/kinetic/potential) are time-invariant. Both halo spin ($\sim$0.031) and anisotropic parameters can be analytically derived. For "small" halos with stable core and slow mass accretion (low peak height $ν$ at late stage of halo life), radial flow vanishes. Small halos rotate with constant angular velocity and non-spin axial dispersion is dominant. Small halos are spherical in shape, incompressible, and isotropic. Radial and azimuthal dispersion are comparable and greater than polar dispersion. Due to finite spin, kinetic energy is not equipartitioned with the greatest energy along azimuthal direction. Different from normal matter, small halos are hotter with faster spin. Halo relaxation from early to late stage involves variation of shape, density, mean flow, momentum, and energy. During relaxation, halo isotopically "stretches" with conserved specific rotational kinetic energy, increasing concentration and momentum of inertial. Halo "stretching" leads to decreasing angular velocity, increasing angular momentum and spin parameter.

astro-ph.GA↗

arXiv2022

Halo mass functions from maximum entropy distributions in collisionless dark matter flow

The halo-mediated inverse mass cascade is a key feature of the intermediate statistically steady state for self-gravitating collisionless dark matter flow (SG-CFD). A broad spectrum of halos and halo groups are necessary to form from inverse mass cascade for long-range interaction system to maximize its entropy. The limiting velocity ($\textbf X$), speed ($\textbf Z$), and energy ($\textbf E$) distributions of collisionless particles can be obtained analytically from a maximum entropy principle. Halo mass function, the distribution of total mass in halos, is a fundamental quantity for structure formation and evolution. Instead of basing mass functions on simplified spherical/elliptical collapse models, it is possible to reformulate mass function as an intrinsic distribution to maximize system entropy during the everlasting statistically steady state. Starting from halo-based description of non-equilibrium dark matter flow, distributions of particle virial dispersion ($\textbf H$), square of particle velocity ($\textbf P$), and number of halos ($\textbf J$) are proposed. Their statistical properties and connections with velocity distribution ($\textbf X$) are well studied and established. With $\textbf H$ being essentially the halo mass function, two limiting cases of $\textbf H$ distribution are analyzed for large halos ($\textbf H_\infty$) and small halos ($\textbf H_s$), respectively. For large halos, $\textbf H_\infty$ is shown to also be a maximum entropy distribution. For small halos, $\textbf H_s$ approximates the $\textbf P$ distribution and recovers the Press-Schechter mass function. The full solution of $\textbf H$ distribution is determined by the velocity distribution ($\textbf X$) that maximizes system entropy and the exact model of halo velocity dispersion.

astro-ph.CO↗

arXiv2022

Micro-cone arrays enhance outcoupling efficiency in horticulture luminescent solar concentrators

Luminescent solar concentrators (LSCs) have shown the ability to realize spectral conversion, which could tailor solar spectrum to better match photosynthesis requirements. However, conventional LSCs are designed to trap, rather than extract, spectrally converted light. Here, we propose an effective method for improving outcoupling efficiency, based on protruded and extruded micro-cone arrays patterned on the bottom surface of LSCs. Using Monte-Carlo ray tracing, we estimate a maximum external quantum efficiency (EQE) of 37.73% for our Horticulture-LSC (HLSC), corresponding to 53.78% improvement relatively to conventional, planar LSCs. Additionally, structured HLSCs provide diffuse light, beneficial for plant growth. Our micro-patterned surfaces provide a solution to light trapping in LSCs and a foundation for practical application of HLSC.

physics.optics↗

arXiv2022

Universality of parametric Coupling Flows over parametric diffeomorphisms

Invertible neural networks based on Coupling Flows CFlows) have various applications such as image synthesis and data compression. The approximation universality for CFlows is of paramount importance to ensure the model expressiveness. In this paper, we prove that CFlows can approximate any diffeomorphism in C^k-norm if its layers can approximate certain single-coordinate transforms. Specifically, we derive that a composition of affine coupling layers and invertible linear transforms achieves this universality. Furthermore, in parametric cases where the diffeomorphism depends on some extra parameters, we prove the corresponding approximation theorems for our proposed parametric coupling flows named Para-CFlows. In practice, we apply Para-CFlows as a neural surrogate model in contextual Bayesian optimization tasks, to demonstrate its superiority over other neural surrogate models in terms of optimization performance.

cs.LG↗

arXiv2021

Latent Space Simulation for Carbon Capture Design Optimization

The CO2 capture efficiency in solvent-based carbon capture systems (CCSs) critically depends on the gas-solvent interfacial area (IA), making maximization of IA a foundational challenge in CCS design. While the IA associated with a particular CCS design can be estimated via a computational fluid dynamics (CFD) simulation, using CFD to derive the IAs associated with numerous CCS designs is prohibitively costly. Fortunately, previous works such as Deep Fluids (DF) (Kim et al., 2019) show that large simulation speedups are achievable by replacing CFD simulators with neural network (NN) surrogates that faithfully mimic the CFD simulation process. This raises the possibility of a fast, accurate replacement for a CFD simulator and therefore efficient approximation of the IAs required by CCS design optimization. Thus, here, we build on the DF approach to develop surrogates that can successfully be applied to our complex carbon-capture CFD simulations. Our optimized DF-style surrogates produce large speedups (4000x) while obtaining IA relative errors as low as 4% on unseen CCS configurations that lie within the range of training configurations. This hints at the promise of NN surrogates for our CCS design optimization problem. Nonetheless, DF has inherent limitations with respect to CCS design (e.g., limited transferability of trained models to new CCS packings). We conclude with ideas to address these challenges.

cs.LG↗

arXiv2021

Local discontinuous Galerkin method on layer-adapted meshes for singularly perturbed reaction-diffusion problems in two dimensions

We analyse the local discontinuous Galerkin (LDG) method for two-dimensional singularly perturbed reaction-diffusion problems. A class of layer-adapted meshes, including Shishkin- and Bakhvalov-type meshes, is discussed within a general framework. Local projections and their approximation properties on anisotropic meshes are used to derive error estimates for energy and "balanced" norms. Here, the energy norm is naturally derived from the bilinear form of LDG formulation and the "balanced" norm is artifically introduced to capture the boundary layer contribution. We establish a uniform convergence of order $k$ for the LDG method using the balanced norm with the local weighted $L^2$ projection as well as an optimal convergence of order $k+1$ for the energy norm using the local Gauss-Radau projections. Numerical experiments are presented.

math.NA↗

arXiv2019

OpenMPR: Recognize Places Using Multimodal Data for People with Visual Impairments

Place recognition plays a crucial role in navigational assistance, and is also a challenging issue of assistive technology. The place recognition is prone to erroneous localization owing to various changes between database and query images. Aiming at the wearable assistive device for visually impaired people, we propose an open-sourced place recognition algorithm OpenMPR, which utilizes the multimodal data to address the challenging issues of place recognition. Compared with conventional place recognition, the proposed OpenMPR not only leverages multiple effective descriptors, but also assigns different weights to those descriptors in image matching. Incorporating GNSS data into the algorithm, the cone-based sequence searching is used for robust place recognition. The experiments illustrate that the proposed algorithm manages to solve the place recognition issue in the real-world scenarios and surpass the state-of-the-art algorithms in terms of assistive navigation performance. On the real-world testing dataset, the online OpenMPR achieves 88.7% precision at 100% recall without illumination changes, and achieves 57.8% precision at 99.3% recall with illumination changes. The OpenMPR is available at https://github.com/chengricky/OpenMultiPR.

cs.CV↗

arXiv2019

Poisson-Boltzmann theory with non-linear ion correlations

The Poisson-Boltzmann (PB) theory is widely used to depict ionic systems. As a mean-field theory, the PB theory neglects the correlation effect in the ionic atmosphere and leads to deviations from experimental results as the concentration or charge valance increases. A modified PB theory including ion correlation effect while retaining its simplicity is critical for many important applications in which ion correlation effect can be significant. In this paper, we present a new model to incorporate ion correlations into the original PB equation by utilizing the Green's function with a non-linear form of the self-energy, which is different from the linear self-energy equation obtained by the Field-Theoretic (FT) approach. Both equations are solved numerically and compared with our molecular dynamics (MD) simulation. The co-ion distribution calculated by the FT approach deviates significantly from the MD simulation, while our results for both counter-ion and co-ion distributions are justified by the MD simulation.

cond-mat.soft↗

arXiv2018

A Stochastic Analysis of Steady and Transient Heat Conduction in Random Media Using a Homogenization Approach

We present a new stochastic analysis for steady and transient one-dimensional heat conduction problem based on the homogenization approach. Thermal conductivity is assumed to be a random field K consisting of random variables of a total large number N. Both steady and transient solutions T are expressed in terms of the homogenized solution and its spatial derivatives, where homogenized solution is obtained by solving the homogenized equation with effective thermal conductivity. Both mean and variance of stochastic solutions can be obtained analytically for K field consisting of identically distributed (i.i.d) random variables. The mean and variance of T are shown to be dependent only on the mean and variance of these i.i.d variables, not the particular form of probability distribution function of i.i.d variables. Variance of temperature field T can be separated into two contributions: the ensemble contribution (through the homogenized temperature ); and the configurational contribution (through different configrations) . The configurational contribution is shown to be proportional to the local gradient of homogenized solution. Large uncertainty of T field was found at locations with large gradient of homogenized solution due to the significant configurational contributions at these locations. Numerical simulations were implemented based on a direct Monte Carlo method and good agreement is obtained between numerical Monte Carlo results and the proposed stochastic analysis.

cond-mat.stat-mech↗

arXiv2018

Simulation of Heterogeneous Atom Probe Tip Shapes Evolution during Field Evaporation Using a Level Set Method and Different Evaporation Models

In atom probe tomography (APT), accurate reconstruction of the spatial positions of field evaporated ions from measured detector patterns depends upon a correct understanding of the dynamic tip shape evolution and evaporation laws of component atoms. Artifacts in APT reconstructions of heterogeneous materials can be attributed to the assumption of homogeneous evaporation of all the elements in the material in addition to the assumption of a steady state hemispherical dynamic tip shape evolution. A level set method based specimen shape evolution model is developed in this study to simulate the evaporation of synthetic layered-structured APT tips. The simulation results of the shape evolution by the level set model qualitatively agree with the finite element method and the literature data using the finite difference method. The asymmetric evolving shape predicted by the level set model demonstrates the complex evaporation behavior of heterogeneous tip and the interface curvature can potentially lead to the artifacts in the APT reconstruction of such materials. Compared with other APT simulation methods, the new method provides smoother interface representation with the aid of the intrinsic sub-grid accuracy. Two evaporation models (linear and exponential evaporation laws) are implemented in the level set simulations and the effect of evaporation laws on the tip shape evolution is also presented.

physics.comp-ph↗

arXiv2018

Modeling Selective Intergranular Oxidation of Binary Alloys

Intergranular attack of alloys under hydrothermal conditions is a complex problem that depends on metal and oxygen transport kinetics via solid-state and channel-like pathways to an advancing oxidation front. Experiments reveal very different rates of intergranular attack and minor element depletion distances ahead of the oxidation front for nickel-based binary alloys depending on the minor element. For example, a significant Cr depletion up to 9 microns ahead of grain boundary crack tips were documented for Ni-5Cr binary alloy, in contrast to relatively moderate Al depletion for Ni-5Al (~100s of nm). We present a mathematical kinetics model that adapts Wagner's model for thick film growth to intergranular attack of binary alloys. The transport coefficients of elements O, Ni, Cr, and Al in bulk alloys and along grain boundaries were estimated from the literature. For planar surface oxidation, a critical concentration of the minor element can be determined from the model where the oxide of minor element becomes dominant over the major element. This generic model for simple grain boundary oxidation can predict oxidation penetration velocities and minor element depletion distances ahead of the advancing front that are comparable to experimental data. The significant distance of depletion of Cr in Ni-5Cr in contrast to the localized Al depletion in Ni-5Al can be explained by the model due to the combination of the relatively faster diffusion of Cr along the grain boundary and slower diffusion in bulk grains, relative to Al.

physics.chem-ph↗

arXiv2018

Phonon excitation and energy redistribution in phonon space for energy transport in one-dimensional lattice with nonlinear dispersion

We first propose fundamental solutions of wave propagation in one-dimensional dispersive chain subject to a localized initial perturbation in the displacement. Analytical solutions are obtained for both second order nonlinear dispersive chain and homogenous harmonic chain. Solution was also compared with numerical results from molecular dynamics (MD) simulations. Locally dominant phonon modes (k-space) are introduced based on these solutions. These locally defined phonon modes k(x,t) spatially and temporally varying with x and t are critical to the establishment of the local thermodynamic equilibrium (LTE). The establishment of LTE should require a uniform distribution of energy in these modes at any given time t and location x. Wave propagation accompanying with the nonequilibrium dynamics leads to the excitation of these locally defined phonon modes. It was found that the system energy is redistributed among these excited phonons modes (k-space). This redistribution process is only possible with nonlinear dispersion and requires a finite amount of time to achieve a steady state distribution depending on the spatial distribution (or frequency content) of initial perturbation and the dispersion relation, where sharper and concentrated perturbation leads to a faster redistribution. Ballistic type of heat transport along the harmonic chain reveals that at any given position the lowest mode (k=0) is excited first and gradually expanding to the highest mode, which can only asymptotically approach the maximum mode of the first Brillouin zone. Energy is shown to be uniformly distributed in all available phonon modes lower than the highest mode. The energy flux along the chain is shown to be a constant with time and proportional to the sound speed (ballistic transport). Comparison with the Fourier's law leads to a time-dependent thermal conductivity that diverges with time.

cond-mat.stat-mech↗